Conformal parameterization using discrete Ricci flow. More...

Classes
struct	Euclid::RicciFlowSolverSettings
	Ricci flow solver settings. More...

class	Euclid::Ricci_flow_parameterizer3< Mesh, SEM, SVM >
	Compute plane parameterization with Ricci flow. More...

Enumerations
enum	Euclid::RicciFlowSolverType { Euclid::RicciFlowSolverType::GradientDescent, Euclid::RicciFlowSolverType::Newton }
	Ricci flow solver types. More...

enum	RicciFlowSolverStatus { Optimal, Suboptimal, InvalidInput }

Functions
template<typename Mesh , typename VertexRadiusMap , typename EdgeWeightMap >
void	Euclid::circle_packing_metric (Mesh &mesh, VertexRadiusMap vrm, EdgeWeightMap ewm)
	Compute the circle packing metric. More...

template<typename Mesh , typename VertexRadiusMap , typename EdgeWeightMap , typename SEM , typename SVM , typename VertexUVMap >
void	Euclid::embed_circle_packing_metric (const Mesh &mesh, VertexRadiusMap vrm, EdgeWeightMap ewm, CGAL::Seam_mesh< Mesh, SEM, SVM > &seam_mesh, VertexUVMap uvm)
	Embed the circle packing metric into plane. More...

template<typename Mesh , typename VertexRadiusMap , typename EdgeWeightMap , typename VertexCurvatureMap >
RicciFlowSolverStatus	Euclid::ricci_flow (Mesh &mesh, VertexRadiusMap vrm, EdgeWeightMap ewm, VertexCurvatureMap vcm, const RicciFlowSolverSettings &settings=RicciFlowSolverSettings())
	The discrete Ricci flow. More...

Detailed Description

Reference

[1] Jin, M., Kim, J., Luo, F., Gu, X. Discrete Surface Ricci Flow.

[2] Yang, YL., Guo, R., Luo, F., Hu, SM., Gu, X. Generalized Discrete Ricci Flow.

Enumeration Type Documentation

strong

Enumerator
GradientDescent	Gradient descent solver.
Newton	Newton solver.

template<typename Mesh , typename VertexRadiusMap , typename EdgeWeightMap >

void Euclid::circle_packing_metric	(	Mesh &	mesh,
		VertexRadiusMap	vrm,
		EdgeWeightMap	ewm
	)

Inverse circle packing metric is used for better robustness.

Parameters

template<typename Mesh , typename VertexRadiusMap , typename EdgeWeightMap , typename SEM , typename SVM , typename VertexUVMap >

void Euclid::embed_circle_packing_metric	(	const Mesh &	mesh,
		VertexRadiusMap	vrm,
		EdgeWeightMap	ewm,
		CGAL::Seam_mesh< Mesh, SEM, SVM > &	seam_mesh,
		VertexUVMap	uvm
	)

The uv-coordinates are stored in the seam mesh.

Parameters

mesh	Input mesh.
vrm	Vertex radius property map.
ewm	Edge weight property map.
seam_mesh	The seam mesh.
uvm	Vertex uv-coordinate property map.

template<typename Mesh , typename VertexRadiusMap , typename EdgeWeightMap , typename VertexCurvatureMap >

RicciFlowSolverStatus Euclid::ricci_flow	(	Mesh &	mesh,
		VertexRadiusMap	vrm,
		EdgeWeightMap	ewm,
		VertexCurvatureMap	vcm,
		const RicciFlowSolverSettings &	settings = `RicciFlowSolverSettings()`
	)

Optimize the given circle packing metric using Ricci flow.

Parameters